Internal resonance of hyperelastic thin-walled cylindrical shells under harmonic axial excitation and time-varying temperature field

Abstract

In this paper, the internal resonance characteristics of hyperelastic cylindrical shells under the time-varying temperature field are investigated for the first time, and the evolution of the isolated bubble is carried out. Through the analysis of the influences of temperature on material parameters, the hyperelastic strain energy density function in the unsteady temperature field is presented. The governing equations describing the axisymmetric nonlinear vibration are derived from the nonlinear thin shell theory and the variational principle. With the harmonic balance method and the arc length method, the steady state solutions of shells are obtained, and their stabilities are determined. The influences of the discrete mode number, structural and temperature parameters on the nonlinear shell behaviors are examined. The role of the parameter variation in evolution behaviors of isolated bubble shaped responses is revealed under the condition of 3:1 internal resonance. The results manifest that both structural and temperature parameters can affect the resonance range of the response curve, and the perturbed temperature has a more significant effect on the stable region of the solution.